Group #24990136 — subgroups

Subgroups — #24990136

Order 11008.

394 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 394 conjugacy classes of subgroups — too many to draw. Only its 99 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19132925	C₂	1	2	yes	maximal
2	#19132501	C₂	1	4	yes	maximal
3	C₄₃×#2313	C₂	1	1	yes	maximal, characteristic
4	#14582863	C₂²	1	4	yes	—
5	#14582625	—	2	4	no	—
6	C₂²×C₄⋊C₄×C₄₃	C₂²	1	1	yes	characteristic
7	C₄₃×#387	—	2	4	no	—
8	C₄₃×#381	C₄	1	2	yes	—
9	C₄₃×#380	C₂²	1	2	yes	—
10	C₄×C₂²⋊C₄×C₄₃	C₄	1	2	yes	—
11	C₂×#10621877	—	2	4	no	—
12	C₂²⋊(C₄₃⋊C₈)	—	2	4	no	—
13	C₂²⋊(C₄₃⋊C₈)	—	2	4	no	—
14	C₂³×C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
15	C₂³×C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
16	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
17	C₂×C₄⋊C₄×C₄₃	—	2	4	no	—
18	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
19	C₂×C₄⋊C₄×C₄₃	D₄	1	4	yes	—
20	C₂×C₂²⋊C₄×C₄₃	C₂×C₄	1	4	yes	—
21	C₂×C₄²×C₄₃	—	2	2	no	—
22	#95×C₄₃	—	2	2	no	—
23	#95×C₄₃	—	2	4	no	—
24	#95×C₄₃	—	2	2	no	—
25	C₂⁴×C₄₃	C₂²×C₄	1	1	yes	characteristic
26	C₂²×C₄×C₄₃	—	2	4	no	—
27	C₂²×C₄×C₄₃	—	2	2	no	—
28	C₂²×C₄×C₄₃	—	2	2	no	—
29	C₂²×C₄×C₄₃	—	4	2	no	—
30	C₂²×C₄×C₄₃	—	8	1	no	—
31	C₂²×C₄×C₄₃	—	8	1	no	—
32	C₂²×C₄×C₄₃	C₂²⋊C₄	1	2	yes	—
33	C₂²×C₄×C₄₃	C₂²⋊C₄	1	2	yes	—
34	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
35	C₂²×C₄×C₄₃	#41	1	4	yes	—
36	C₄⋊C₄×C₄₃	—	2	8	no	—
37	C₄⋊C₄×C₄₃	—	8	2	no	—
38	C₂²⋊C₄×C₄₃	—	4	4	no	—
39	C₄²×C₄₃	—	8	2	no	—
40	#10621877	—	8	4	no	—
41	C₂×C₄₃⋊C₈	—	4	4	no	—
42	C₂³×C₄₃	—	2	2	no	—
43	C₂³×C₄₃	—	4	1	no	—
44	C₂³×C₄₃	—	4	1	no	—
45	C₂³×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
46	C₂³×C₄₃	#117	1	2	yes	—
47	C₂×C₄×C₄₃	—	2	2	no	—
48	C₂×C₄×C₄₃	—	2	2	no	—
49	C₂×C₄×C₄₃	—	2	4	no	—
50	C₂×C₄×C₄₃	—	4	4	no	—
51	C₂×C₄×C₄₃	—	4	2	no	—
52	C₂×C₄×C₄₃	—	4	4	no	—
53	C₂×C₄×C₄₃	—	4	2	no	—
54	C₂×C₄×C₄₃	—	4	4	no	—
55	C₂×C₄×C₄₃	—	4	4	no	—
56	C₂×C₄×C₄₃	—	4	4	no	—
57	C₂×C₄×C₄₃	—	8	2	no	—
58	C₂×C₄×C₄₃	#123	1	4	yes	—
59	C₄₃⋊C₈	—	8	4	no	—
60	#8758	—	43	1	no	maximal, Sylow
61	C₂²×C₄₃	—	2	1	no	—
62	C₂²×C₄₃	—	2	1	no	—
63	C₂²×C₄₃	—	2	2	no	—
64	C₂²×C₄₃	—	2	2	no	—
65	C₂²×C₄₃	—	2	2	no	—
66	C₂²×C₄₃	—	4	4	no	—
67	C₂²×C₄₃	#381	1	1	yes	characteristic
68	C₂²×C₄₃	#413	1	2	yes	—
69	C₄×C₄₃	—	2	4	no	—
70	C₄×C₄₃	—	4	2	no	—
71	C₄×C₄₃	—	4	2	no	—
72	C₄×C₄₃	—	8	4	no	—
73	#2313	D₄₃	1	1	yes	characteristic
74	#1463	—	43	2	no	—
75	#1305	—	43	4	no	—
76	C₂×C₄₃	—	2	2	no	—
77	C₂×C₄₃	—	4	2	no	—
78	C₂×C₄₃	#1822	1	1	yes	characteristic
79	C₂×C₄₃	#1828	1	1	yes	characteristic
80	C₂×C₄₃	#1830	1	1	yes	characteristic
81	C₂²×C₄⋊C₄	C₂×D₄₃	1	1	yes	characteristic
82	#407	—	43	4	no	—
83	#387	—	2	4	no	—
84	#381	Dic₄₃	1	2	yes	—
85	#380	C₂×D₄₃	1	2	yes	—
86	C₄×C₂²⋊C₄	Dic₄₃	1	2	yes	—
87	#324	—	86	4	no	—
88	C₄₃	#8758	1	1	yes	characteristic, complemented, Sylow
89	C₂³×C₄	C₂×Dic₄₃	1	1	yes	characteristic
90	C₂³×C₄	C₂×Dic₄₃	1	1	yes	characteristic
91	C₂³×C₄	C₂²×D₄₃	1	1	yes	characteristic
92	C₂×M₁₆	—	86	4	no	—
93	C₂×C₄⋊C₄	—	2	4	no	—
94	C₂×C₄⋊C₄	—	2	2	no	—
95	C₂×C₄⋊C₄	C₂²⋊D₄₃	1	4	yes	—
96	C₂×C₂²⋊C₄	C₂×Dic₄₃	1	4	yes	—
97	C₂×C₄²	—	2	2	no	—
98	C₂²⋊C₈	—	86	4	no	—
99	C₂²⋊C₈	—	86	4	no	—
100	#95	—	2	2	no	—
101	#95	—	2	4	no	—
102	#95	—	2	2	no	—
103	C₂⁴	C₂²×Dic₄₃	1	1	yes	characteristic
104	C₂²×C₄	—	2	2	no	—
105	C₂²×C₄	—	2	2	no	—
106	C₂²×C₄	—	2	4	no	—
107	C₂²×C₄	—	4	2	no	—
108	C₂²×C₄	—	8	1	no	—
109	C₂²×C₄	—	8	1	no	—
110	C₂²×C₄	C₂²⋊Dic₄₃	1	2	yes	—
111	C₂²×C₄	C₂²⋊Dic₄₃	1	2	yes	—
112	C₂²×C₄	#10621898	1	4	yes	—
113	C₂²×C₄	C₂×C₂²⋊D₄₃	1	2	yes	—
114	M₁₆	—	344	4	no	—
115	C₂×C₈	—	172	4	no	—
116	C₄⋊C₄	—	2	8	no	—
117	C₄⋊C₄	—	8	2	no	—
118	C₂²⋊C₄	—	4	4	no	—
119	C₄²	—	8	2	no	—
120	C₂³	—	2	2	no	—
121	C₂³	—	4	1	no	—
122	C₂³	—	4	1	no	—
123	C₂³	C₂×C₂²⋊Dic₄₃	1	1	yes	characteristic
124	C₂³	#13063284	1	2	yes	—
125	C₂×C₄	—	2	4	no	—
126	C₂×C₄	—	2	2	no	—
127	C₂×C₄	—	2	2	no	—
128	C₂×C₄	—	4	2	no	—
129	C₂×C₄	—	4	4	no	—
130	C₂×C₄	—	4	4	no	—
131	C₂×C₄	—	4	2	no	—
132	C₂×C₄	—	4	4	no	—
133	C₂×C₄	—	4	4	no	—
134	C₂×C₄	—	4	4	no	—
135	C₂×C₄	—	8	2	no	—
136	C₂×C₄	#13063308	1	4	yes	—
137	C₈	—	344	4	no	—
138	C₂²	—	2	1	no	—
139	C₂²	—	2	1	no	—
140	C₂²	—	2	2	no	—
141	C₂²	—	2	2	no	—
142	C₂²	—	2	2	no	—
143	C₂²	—	4	4	no	—
144	C₂²	#14582762	1	1	yes	characteristic
145	C₂²	#14582883	1	2	yes	—
146	C₄	—	2	4	no	—
147	C₄	—	4	2	no	—
148	C₄	—	4	2	no	—
149	C₄	—	8	4	no	—
150	C₂	—	2	2	no	—
151	C₂	—	4	2	no	—
152	C₂	#19134678	1	1	yes	characteristic
153	C₂	#19134703	1	1	yes	characteristic
154	C₂	#19134709	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#19132925

C₂

yes

maximal

#19132501

C₂

yes

maximal

C₄₃×#2313

C₂

yes

maximal, characteristic

#14582863

C₂²

yes

—

#14582625

—

C₂²×C₄⋊C₄×C₄₃

C₂²

yes

characteristic

C₄₃×#387

—

C₄₃×#381

C₄

yes

—

C₄₃×#380

C₂²

yes

—

C₄×C₂²⋊C₄×C₄₃

C₄

yes

—

C₂×#10621877

—

C₂²⋊(C₄₃⋊C₈)

—

C₂²⋊(C₄₃⋊C₈)

—

C₂³×C₄×C₄₃

C₂×C₄

yes

characteristic

C₂³×C₄×C₄₃

C₂×C₄

yes

characteristic

C₂³×C₄×C₄₃

C₂³

yes

characteristic

C₂×C₄⋊C₄×C₄₃

—

C₂×C₄⋊C₄×C₄₃

—

C₂×C₄⋊C₄×C₄₃

D₄

yes

—

C₂×C₂²⋊C₄×C₄₃

C₂×C₄

yes

—

C₂×C₄²×C₄₃

—

#95×C₄₃

—

#95×C₄₃

—

#95×C₄₃

—

C₂⁴×C₄₃

C₂²×C₄

yes

characteristic

C₂²×C₄×C₄₃

—

C₂²×C₄×C₄₃

—

C₂²×C₄×C₄₃

—

C₂²×C₄×C₄₃

—

C₂²×C₄×C₄₃

—

C₂²×C₄×C₄₃

—

C₂²×C₄×C₄₃

C₂²⋊C₄

yes

—

C₂²×C₄×C₄₃

C₂²⋊C₄

yes

—

C₂²×C₄×C₄₃

C₂×D₄

yes

—

C₂²×C₄×C₄₃

#41

yes

—

C₄⋊C₄×C₄₃

—

C₄⋊C₄×C₄₃

—

C₂²⋊C₄×C₄₃

—

C₄²×C₄₃

—

#10621877

—

C₂×C₄₃⋊C₈

—

C₂³×C₄₃

—

C₂³×C₄₃

—

C₂³×C₄₃

—

C₂³×C₄₃

C₂×C₂²⋊C₄

yes

characteristic

C₂³×C₄₃

#117

yes

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

#123

yes

—

C₄₃⋊C₈

—

#8758

—

maximal, Sylow

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

#381

yes

characteristic

C₂²×C₄₃

#413

yes

—

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

—

#2313

D₄₃

yes

characteristic

#1463

—

#1305

—

C₂×C₄₃

—

C₂×C₄₃

—

C₂×C₄₃

yes

C₂×C₄₃

yes

C₂×C₄₃

yes

C₂²×C₄⋊C₄

C₂×D₄₃

yes

—

—

Dic₄₃

yes

—

#380

C₂×D₄₃

yes

—

C₄×C₂²⋊C₄

Dic₄₃

yes

—

#324

—

C₄₃

#8758

yes

characteristic, complemented, Sylow

C₂³×C₄

C₂×Dic₄₃

yes

characteristic

C₂³×C₄

C₂×Dic₄₃

yes

characteristic

C₂³×C₄

C₂²×D₄₃

yes

characteristic

C₂×M₁₆

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

C₂²⋊D₄₃

yes

—

C₂×C₂²⋊C₄

C₂×Dic₄₃

yes

—

C₂×C₄²

—

C₂²⋊C₈

—

C₂²⋊C₈

—

100

#95

—

101

#95

—

102

#95

—

103

C₂⁴

C₂²×Dic₄₃

yes

characteristic

104

C₂²×C₄

—

105

C₂²×C₄

—

106

C₂²×C₄

—

107

C₂²×C₄

—

108

C₂²×C₄

—

109

C₂²×C₄

—

110

C₂²×C₄

C₂²⋊Dic₄₃

yes

—

111

C₂²×C₄

C₂²⋊Dic₄₃

yes

—

112

C₂²×C₄

#10621898

yes

—

113

C₂²×C₄

C₂×C₂²⋊D₄₃

yes

—

114

M₁₆

—

344

—

115

C₂×C₈

—

172

—

116

C₄⋊C₄

—

117

C₄⋊C₄

—

118

C₂²⋊C₄

—

119

C₄²

—

120

C₂³

—

121

C₂³

—

122

C₂³

—

123

C₂³

C₂×C₂²⋊Dic₄₃

yes

characteristic

124

C₂³

#13063284

yes

—

125

C₂×C₄

—

126

C₂×C₄

—

127

C₂×C₄

—

128

C₂×C₄

—

129

C₂×C₄

—

130

C₂×C₄

—

131

C₂×C₄

—

132

C₂×C₄

—

133

C₂×C₄

—

134

C₂×C₄

—

135

C₂×C₄

—

136

C₂×C₄

#13063308

yes

—

137

C₈

—

344

—

138

C₂²

—

139

C₂²

—

140

C₂²

—

141

C₂²

—

142

C₂²

—

143

C₂²

—

144

C₂²

#14582762

yes

characteristic

145

C₂²

#14582883

yes

—

146

C₄

—

147

C₄

—

148

C₄

—

149

C₄

—

150

C₂

—

151

C₂

—

152

C₂

#19134678

yes

characteristic

153

C₂

#19134703

yes

characteristic

154

C₂

#19134709

yes

characteristic

	subgroup	G/H
center	C₂²	#14582762
commutator, prime radical	C₂⁴×C₄₃	C₂²×C₄
Frattini	C₂³×C₄	C₂²×D₄₃
Fitting	C₄₃×#2313	C₂
socle	C₂²×C₄₃	#381
cosocle	C₂³×C₄×C₄₃	C₂³
hypercenter	#2313	D₄₃
hypocenter	C₄₃	#8758
LCS	G ▷ C₂⁴×C₄₃ ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₂³×C₄ ◁ #2313

subgroup

G/H

center

C₂²

#14582762

commutator, prime radical

C₂⁴×C₄₃

C₂²×C₄

Frattini

C₂³×C₄

C₂²×D₄₃

Fitting

C₄₃×#2313

C₂

socle

C₂²×C₄₃

#381

cosocle

C₂³×C₄×C₄₃

C₂³

D₄₃

C₄₃

G ▷ C₂⁴×C₄₃ ▷ C₂²×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂² ◁ C₂³×C₄ ◁ #2313

N	H ≅ G/N	type
88. C₄₃	#8758	semidirect

H ≅ G/N

type

88. C₄₃

#8758

semidirect

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
#19132925	2
#19132501	2
C₄₃×#2313	2
#8758	43

subgroup

index

#19132925

#19132501

C₄₃×#2313

#8758

Subgroups — #24990136

Conjugacy classes of subgroups

Complements

Maximal subgroups